The spatially homogeneous relativistic Boltzmann equation with a hard potential

TL;DR

This paper investigates the existence of global solutions to the relativistic Boltzmann equation with hard potentials in Minkowski and Robertson-Walker spacetimes, extending classical inequalities to the relativistic context.

Contribution

It introduces a relativistic Povzner inequality and proves global existence results for hard potential collision cross sections in specific spacetimes.

Findings

Global solutions exist for certain hard potential collision cross sections.

The relativistic Povzner inequality is established.

Results apply to Minkowski and Robertson-Walker spacetimes.

Abstract

In this paper, we study spatially homogeneous solutions of the Boltzmann equation in special relativity and in Robertson-Walker spacetimes. We obtain an analogue of the Povzner inequality in the relativistic case and use it to prove global existence theorems. We show that global solutions exist for a certain class of collision cross sections of the hard potential type in Minkowski space and in spatially flat Robertson-Walker spacetimes.